Read more
Informationen zum Autor Kenneth S. Williams is currently Professor Emeritus and Distinguished Research Professor of Mathematics at Carleton University, Ottawa. Klappentext A gentle introduction to Liouville's powerful method in elementary number theory. Suitable for advanced undergraduate and beginning graduate students. Zusammenfassung The only book entirely devoted to Joseph Liouville's elementary method in number theory! this gentle introduction explains his method in a clear and straightforward manner! including many applications. This is an extremely valuable resource suitable for advanced undergraduate and beginning graduate students! and researchers in number theory. Inhaltsverzeichnis Preface; 1. Joseph Liouville (1809-1888); 2. Liouville's ideas in number theory; 3. The arithmetic functions ¿k(n), ¿k*(n), dk,m(n) and Fk(n); 4. The equation i2 + jk = n; 5. An identity of Liouville; 6. A recurrence relation for ¿*(n); 7. The Girard-Fermat theorem; 8. A second identity of Liouville; 9. Sums of two, four and six squares; 10. A third identity of Liouville; 11. Jacobi's four squares formula; 12. Besge's formula; 13. An identity of Huard, Ou, Spearman and Williams; 14. Four elementary arithmetic formulae; 15. Some twisted convolution sums; 16. Sums of two, four, six and eight triangular numbers; 17. Sums of integers of the form x2+xy+y2; 18. Representations by x2+y2+z2+2t2, x2+y2+2z2+2t2 and x2+2y2+2z2+2t2; 19. Sums of eight and twelve squares; 20. Concluding remarks; References; Index.
